For what it's worth, here is the basic philosophy of our flight department...
The autopilot, like any other tool at our disposal, can be properly used and it can also be dangerously abused. As professionals, we would like to believe that we can all hand fly all the various types of approaches down to their respective minimums correctly and proficiently without any type of aid - flight director, autopilot, etc. If we can't do that, then we need to either get more training or change professions - period. That being said, we spend great sums of money to provide redundancies for nearly every system on our aircraft - multi engines, dual this, triple that, etc., etc. When we hand fly an ILS approach down to minimums, what redundancy to we have in case of "pilot failure"? If the PNF is doing his job is he going to be able to effectively take the controls in the case of a botched approach? Obviously not, and even if he were able to, is solid IFR at 200' AGL and with a 700 fpm sink rate the time and place to be making those types of changes?
I believe that we can and should hand fly all of the "high and mid" minimums approaches we want, but when the ceiling gets below 500 feet and the visibility gets below a mile couple it up and let the autopilot do its thing. We then become the backup to the autopilot and we have injected an element of redundancy into the operation. In that rare case that the autopilot messes up and gets us sideways to the world, relief is only a click of the button away. In the mean time, you've been able to watch and monitor the approach while covering the controls. If it ever becomes necessary, the transition is both instantaneous and seamless. In reality, how many time per year do we actually fly approached right down to minimums? Not very many. I'd say that we actually run more of a chance to have a pilot screwup than an autopilot failure.
We've all flown with those hairy chested pilots who say that "real" pilots don't use auto pilots. I'm sorry, I don't buy it. Real pilots know when to use them and when not to and we're just not talking during approaches either. There are other times when we probably have no business hand flying our high performance turbine-powered aircraft. For example, below 10,000' MSL on VFR days. Can you really hand fly your aircraft while maintaining an adequate watch for traffic?